Multiband and nonlinear hopping corrections to the three-dimensional Bose-Fermi-Hubbard model

Recent experiments revealed the importance of higher-band effects for the Mott-insulator(MI)-superfluid transition(SF) of ultracold bosonic atoms or mixtures of bosons and fermions in deep optical lattices [ Best et al., Phys. Rev. Lett. 102, 030408 (2009); Will et al., Nature (London) 465, 197 (2010)]. In the present work we derive an effective lowest-band Hamiltonian in three dimensions that generalizes the standard Bose-Fermi-Hubbard model taking these effects as well as nonlinear corrections of the tunneling amplitudes mediated by interspecies interactions into account. It is shown that a correct description of the lattice states in terms of the bare-lattice Wannier functions, rather than approximations such as harmonic-oscillator states, is essential. In contrast to self-consistent approaches based on effective Wannier functions, our approach captures the observed reduction of the superfluid phase for repulsive interspecies interactions.